Adaptive Control Tutorial (Advances in Design and Control)

403 Pages·2006·18.18 MB·english

by  Petros Ioannou and Baris Fidan

Adaptive
Control
Tutorial
Advances in Design and Control
SIAM's Advances in Design and Control series consists of texts and monographs dealing with all
areas of design and control and their applications. Topics of interest include shape optimization,
multidisciplinary design, trajectory optimization, feedback, and optimal control. The series focuses
on the mathematical and computational aspects of engineering design and control that are usable
in a wide variety of scientific and engineering disciplines.
Editor-in-Chief
Ralph C. Smith, North Carolina State University
Editorial Board
Athanasios C. Antoulas, Rice University
Siva Banda, Air Force Research Laboratory
Belinda A. Batten, Oregon State University
John Betts, The Boeing Company
Christopher Byrnes, Washington University
Stephen L. Campbell, North Carolina State University
Eugene M. Cliff, Virginia Polytechnic Institute and State University
Michel C. Delfour, University of Montreal
Max D. Gunzburger, Florida State University
J. William Helton, University of California, San Diego
Mary Ann Horn, Vanderbilt University
Arthur J. Krener, University of California, Davis
Kirsten Morris, University of Waterloo
Richard Murray, California Institute of Technology
Anthony Patera, Massachusetts Institute of Technology
Ekkehard Sachs, University of Trier
Allen Tannenbaum, Georgia Institute of Technology
Series Volumes
loannou, Petros, and Fidan, Bans, Adaptive Control Tutorial
Bhaya, Amit, and Kaszkurewicz, Eugenius, Control Perspectives on Numerical Algorithms and
Matrix Problems
Robinett III, Rush D., Wilson, David G., Eisler, G. Richard, and Hurtado, John E., Applied Dynamic
Programming for Optimization of Dynamical Systems
Huang, J., Nonlinear Output Regulation: Theory and Applications
Haslinger, J. and Makinen, R. A. E., Introduction to Shape Optimization: Theory, Approximation,
and Computation
Antoulas, Athanasios C., Approximation of Large-Scale Dynamical Systems
Gunzburger, Max D., Perspectives in Flow Control and Optimization
Delfour, M. C. and Zolesio, J.-P., Shapes and Geometries: Analysis, Differential Calculus, and
Optimization
Betts, John T., Practical Methods for Optimal Control Using Nonlinear Programming
El Ghaoui, Laurent and Niculescu, Silviu-lulian, eds., Advances in Linear Matrix Inequality Methods
in Control
Helton, J. William and James, Matthew R., Extending H°°Control to Nonlinear Systems: Control
of Nonlinear Systems to Achieve Performance Objectives
Adaptive
Control
Tutorial
Petros loannou
University of Southern California
Los Angeles, California
Baris Fidan
National ICT Australia & Australian National University
Canberra, Australian Capital Territory, Australia
siam
Society for Industrial and Applied Mathematics
Philadelphia
Copyright © 2006 by the Society for Industrial and Applied Mathematics.
10987654321
All rights reserved. Printed in the United States of America. No part of this book may
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Trademarked names may be used in this book without the inclusion of a trademark symbol.
These names are used in an editorial context only; no infringement of trademark is intended.
MATLAB is a registered trademark of The MathWorks, Inc. For MATLAB product information,
please contact The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA,
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Library of Congress Cataloging-in-Publication Data
loannou, P. A. (Petros A.), 1953-
Adaptive control tutorial / Petros loannou, Baris Fidan.
p. cm. - (Advances in design and control)
Includes bibliographical references and index.
ISBN-13: 978-0-89871-615-3 (pbk.)
ISBN-10: 0-89871-615-2 (pbk.)
1. Adaptive control systems. I. Fidan, Baris. II. Title.
TJ217.1628 2006
629.8'36-dc22
2006051213
siam
is a registered trademark.
To Kira and Andreas
P.I.
To my family
B.F.
This page intentionally left blank
Contents
Preface xi
Acknowledgments xiii
List of Acronyms xv
1 Introduction 1
1.1 Adaptive Control: Identifier-Based 2
1.2 Adaptive Control: Non-Identifier-Based 5 5
1.2.1 Gain Scheduling 5
1.2. 2 Multiple Models, Search Methods, and Switching Schemes 6
1.3 Why Adaptive Control 7
1.4 A Brief History 9
2 Parametric Models 13
Problems 22
3 Parameter Identification: Continuous Time 25
3.1 Introduction 25
3.2 Example: One-Parameter Case 26
3.3 Example: Two Parameters 30
3.4 Persistence of Excitation and Sufficiently Rich Inputs 31
3.5 Example: Vector Case 34
3.6 Gradient Algorithms Based on the Linear Model 36
3.6.1 Gradient Algorithm with Instantaneous Cost Function . . 37
3.6.2 Gradient Algorithm with Integral Cost Function 41
3.7 Least-Squares Algorithms 42
3.7.1 Recursive LS Algorithm with Forgetting Factor 44
3.7.2 Pure LS Algorithm 45
3.7.3 Modified LS Algorithms 47
3.8 Parameter Identification Based on DPM 48
3.9 Parameter Identification Based on B-SPM 50
3.10 Parameter Projection 52
3.11 Robust Parameter Identification 55
3.11.1 Instability Example 56
vii
viii Contents
3.11.2 Dominantly Rich Excitation 57
3.12 Robust Adaptive Laws 62
3.12.1 Dynamic Normalization 63
3.12.2 Robust Adaptive Laws: a-Modification 65
3.12.3 Parameter Projection 71
3.12.4 Dead Zone 73
3.13 State-Space Identifiers 75
3.14 Adaptive Observers 78
3.15 Case Study: Users in a Single Bottleneck Link Computer Network . . 80
Problems 82
4 Parameter Identification: Discrete Time 91
4.1 Introduction 91
4.2 Discretization of Continuous-Time Adaptive Laws 95
4.3 Discrete-Time Parametric Model 96
4.4 Sufficiently Rich Inputs 97
4.5 Gradient Algorithms 99
4.5.1 Projection Algorithm 99
4.5.2 Gradient Algorithm Based on Instantaneous Cost 101
4.6 LS Algorithms 102
4.6.1 Pure LS 102
4.7 Modified LS Algorithms 107
4.8 Parameter Identification Based on DPM 109
4.9 Parameter Identification Based on B-SPM 109
4.10 Parameter Projection 109
4.11 Robust Parameter Identification 114
4.11.1 Dominantly Rich Excitation 114
4.11.2 Robustness Modifications 116
4.11.3 Parameter Projection 121
4.12 Case Study: Online Parameter Estimation of Traffic Flow
Characteristics 123
Problems 127
5 Continuous-Time Model Reference Adaptive Control 131
5.1 Introduction 131
5.2 Simple MRAC Schemes 134
5.2.1 Scalar Example: Adaptive Regulation 134
5.2.2 Scalar Example: Direct MRAC without Normalization . . 136
5.2.3 Scalar Example: Indirect MRAC without Normalization . 139
5.2.4 Scalar Example: Direct MRAC with Normalization . . . 141
5.2.5 Scalar Example: Indirect MRAC with Normalization . . 145
5.2.6 Vector Case: Full-State Measurement 149
5.3 MRC for SISO Plants 151
5.3.1 Problem Statement 151
5.3.2 MRC Schemes: Known Plant Parameters 153
5.4 Direct MRAC with Unnormalized Adaptive Laws 158
Contents ix
5.4.1 Relative Degree n* = 1 159
5.4.2 Relative Degree n* = 2 162
5.4.3 Relative Degree Greater than 2 165
5.5 Direct MRAC with Normalized Adaptive Laws 166
5.6 Indirect MRAC 168
5.6.1 Indirect MRAC with Unnormalized Adaptive Laws . . . 169
5.6.2 Indirect MRAC with Normalized Adaptive Law 171
5.7 Robust MRAC 173
5.7.1 MRC: Known Plant Parameters 173
5.7.2 Robust Direct MRAC 177
5.8 Case Study: Adaptive Cruise Control Design 189
5.9 Case Study: Adaptive Attitude Control of a Spacecraft 193
Problems 199
6 Continuous-Time Adaptive Pole Placement Control 207
6.1 Introduction 207
6.2 Simple APPC Schemes: Without Normalization 208
6.2.1 Scalar Example: Adaptive Regulation 208
6.2.2 Scalar Example: Adaptive Tracking 212
6.3 APPC Schemes: Polynomial Approach 215
6.4 APPC Schemes: State-Space Approach 222
6.5 Adaptive Linear Quadratic Control (ALQC) 227
6.6 Stabilizability Issues and Modified APPC 231
6.6.1 Loss of Stabilizability: A Simple Example 231
6.6.2 Modified APPC Schemes 232
6.7 Robust APPC Schemes 235
6.7.1 PPC: Known Parameters 236
6.7.2 Robust Adaptive Laws for APPC Schemes 238
6.7.3 Robust APPC: Polynomial Approach 239
6.8 Case Study: ALQC Design for an F-16 Fighter Aircraft 242
6.8.1 LQ Control Design with Gain Scheduling 245
6.8.2 Adaptive LQ Control Design 246
6.8.3 Simulations 246
Problems 249
7 Adaptive Control for Discrete-Time Systems 255
7.1 Introduction 255
7.2 MRAC 255
7.2.1 Scalar Example 255
7.2.2 General Case: MRC 258
7.2.3 Direct MRAC 261
7.2.4 Indirect MRAC 264
7.3 Adaptive Prediction and Control 266
7.3.1 Adaptive One-Step-Ahead Control 271
7.4 APPC 272
Problems 275